Dynamic analysis: Effect of damping on frequency

Please can anyone explain the effect of damping on frequency? Whether, damping increases or decreases the frequency and why? An explanation with a physical interpretation will be gratefully appreciated.

A lightly damped oscillator has a frequency very close to the natural one (without damping).
As damping grows, the "efective" frequency gets smaller and vanishes when the damping reaches the critical value.

Consider the case where the damping approached infinity, you can see that the motion of the oscillator would all but vanish.
Another way to think about it would be to see that damping removes energy from the oscillator so its return trip from an extreme value will take longer than the time it took getting there from the zero point.